Significant Figures

What is a significant figure?  There are 2 kinds of numbers:  Exact: the amount of money in your account. Known with certainty.

What is a significant figure?  Approximate: weight, height—anything MEASURED. No measurement is perfect.

When to use Significant figures  When a measurement is recorded only those digits that are dependable are written down.

When to use Significant figures  If you measured the width of a paper with your ruler you might record 21.7cm. To a mathematician 21.70, or is the same.

But, to a scientist 21.7cm and 21.70cm is NOT the same  cm to a scientist means the measurement is accurate to within one thousandth of a cm.

How do I know how many Sig Figs?  Rule: Any non-zero numbers will ALWAYS be significant.

How do I know how many Sig Figs?  Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

How many sig figs?  7  40  0.5   7 x 10 5  7,000,000 11 11 11 11 11 11

How do I know how many Sig Figs?  Rule: If zeros are sandwiched between non-zero numbers, the zeros become significant.

How do I know how many Sig Figs?  Rule: If zeros are at the end of a number that has a decimal, the zeros are significant.  These zeros just show how accurate the measurements or calculations are.

How many sig figs here?  1.2  204   4.00   7,083,000,000 22 33 44 33 33 44

How many sig figs here?  3401  2100   5.00   8,000,050,000 44 22 55 33 33 66

What about calculations with sig figs?  Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples  2.45cm + 1.2cm = 3.65cm,  Round off to = 3.7cm  7.432cm + 2cm = 9.432

Multiplication and Division  Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples  cm x 2.45cm = cm 2  Round to  139cm 2  75.8cm x 9.6 cm = cm 2  Round to 730